It is well established that stars are formed by gravitational collapse of molecular cloud cores. Collapsing cores initially undergo isothermal collapse. The isothermal condition breaks down at the density of ˜ 10-13 g cm-3, and the temperature starts rising. Increasing gas pressure decelerates the contraction, and the cores come to hydrostatic equilibrium with a radius of a few AU and a mass of ˜ 0.01 Mȯ, which is called the first cores (e.g. Larson 1969). Observation of the first cores is important but challenging, since their lifetime is short (˜ 1000 yr). The mechanical property of the first cores have been studied by multi-dimensional hydrodynamic calculations considering interstellar magnetic fields and radiative transfer (e.g. Tomisaka 2002; Machida et al.2008; Tomida et al. 2010). In contrast, their chemical property is yet to be understood. It is important to reveal their chemical property in terms of which lines we should use to observe the first cores. In addition, the first cores evolve to protoplanetary disks (Saigo et al. 2008; Machida et al. 2010), hence the compositions of the first cores restrict the initial compositions of disks. We investigate molecular evolution of star forming cores that are initially rotating molecular cloud cores and collapse to form the first cores. The results of three dimensional hydrodynamic calculations (Matsumoto & Hanawa 2003) are adopted as physical models of the core. We trace trajectories of test particles in the hydrodynamic calculations, and molecular evolution is solved using low temperature chemical network (Garrod & Herbst 2006) at T < 100 K and high temperature network (Harada et al. 2010) at T > 100 K along the trajectories. We also consider three body reactions and collisional dissociations (Willacy et al. 1998). Trace particles fall into the first core almost spherically, and rotate in the first core where the spiral arms transports angular momentum. In our model with barotropic approximation, we find that in outer regions (R > 5 AU), the composition is similar to the low temperature chemistry. In intermediate regions (R ˜3 AU), hot-core like species, such as HCOOCH_3 and CH_3OCH_3 are generated. In central regions (R < 1 AU), complex molecules, such as HC_7N, HC_9N and NH_2CN, are formed in the gas phase.Read less <